Computer Aided Design (CAD) systems are used to design and simulate virtual models of electrical, electronic or mechanical devices prior to producing actual physical devices. CAD systems are interactive software tools that run on a digital computer with a graphical display device. In particular, micro-fabricated devices such as electronic integrated circuits (ICs) and Micro Electro-Mechanical Systems (MEMS) can be designed and simulated using CAD systems prior to beginning the costly and time-consuming process of fabricating actual physical devices.
MEMS are micro or nano-scale devices typically fabricated in a similar fashion as integrated circuits (ICs) to exploit the miniaturization, integration, and batch processing attainable with semiconductor manufacturing processes. Unlike ICs which consist solely of electrical components, MEMS devices combine components from multiple physical domains and may contain, for example, electrical, mechanical, and fluidic components. MEMS devices appear in many forms and may include micro-electromechanical sensors and actuators such as gyroscopes, accelerometers, and pressure sensors, micro-fluidic devices such as ink jet heads, Radio-Frequency (RF) devices such as switches, resonators and passives, and optical devices such as micro-mirrors and fiber alignment devices.
The behavior of both MEMS and IC devices can be modeled at the system level as an interconnected network of simpler components. The MEMS device is represented by a network of components such as mechanical beams, plates, electrodes, magnetic coils etc. Each component has an underlying mathematical description, or behavioral model, which is referred to herein as a component model. Typically, these component models are parameterized, i.e. they take as input a few parameters such as width and height, so that the same mathematical model can be used for different versions of the same type of component. For example, a single component may be used to generate models for different dimensions. A system-level simulator numerically computes, or simulates, the collective behavior of the network of component models.
Two commonly used methods of describing a system-level simulation are circuit simulation and signal-flow simulation. A system-level design is captured graphically in a circuit schematic or in a signal-flow diagram, and then its behavior is simulated by, respectively, a circuit simulator or a signal-flow simulator. Traditionally, circuit simulation has been used for electronic circuit design while signal-flow simulation has been used for control system and signal processing design. Currently, both types of system-level simulation are used to simulate not only ICs, but also multi-physics devices such as MEMS.
Schematic driven MEMS simulations, while very useful for initial design purposes, involve approximations that must be verified by detailed 3D numerical analysis of the governing PDEs. Numerical PDE solvers take as input a discrete element model that consists of a mesh representation of the device geometry and some constraints such as boundary conditions or initial conditions. Typically, a user creates the mesh representation by subdividing the geometric shapes that comprise the device into smaller, simpler shapes called elements. The elements are called finite elements if they represent a portion of a 3D solid, or boundary elements if they represent a portion of a surface that encloses a 3D solid. A set of elements that collectively represents an entire device is known as a mesh. Numerical PDE solvers, which may be based on the finite element method (FEM), boundary element method (BEM), or a hybrid of the two, are used to obtain detailed, 3D solution fields such as displacement, stress, and electrostatic charge distribution, and integral quantities such as the resonant frequency, damping force, and total capacitance. Abaqus from Abaqus, Inc. of Pawtucket, R.I. and Ansys from Ansys, Inc. of Canonsburg, Pa. are examples of two commercially available finite element solvers. CoventorWare from Coventor, Inc. of Cary, N.C., is an example of commercially available software that exploits a hybrid FEM/BEM approach to numerically solve the PDEs that describe coupled electromechanics effects in MEMS devices.
Conventional CAD systems allow a user to specify the mesh characteristics, run a mesh generation procedure, and finally run a numerical PDE simulation. Unfortunately, the process of preparing a mesh in conventional CAD systems has several drawbacks. Numerical PDE analysis tends to be very resource intensive from a computer standpoint, requiring considerable memory and processing time. The resource requirements and the quality of the numerical simulation depend largely on the type of finite elements used and the mesh density (level of solid model discretization). Various finite element types, such as tetrahedral, hexahedral, brick, shell and beam elements, are available. Each element type has strengths and weaknesses in its ability to conform to certain geometric shapes, the amount of computational effort required, and accuracy. Using too fine a mesh or inappropriate element types can easily lead to impractically large memory and simulation time requirements. For example, long thin tethers that are typical of MEMS devices can be most efficiently modeled by beam elements as opposed to hexahedral or tetrahedral elements. Likewise, thin plate-like structures that have many perforations can be most efficiently modeled by a collection of interconnected beam elements.
The choice of element type in preparing a model for meshing may be left to the user, who must apply considerable subjective judgment. Alternatively, an automatic mesh generation algorithm may automatically attempt to choose the most appropriate element type for a mesh. Unfortunately, automatic algorithms require an extensive set of heuristics and therefore are inherently unreliable since they are not aware of the purpose and shape of sub-structures within the design and are unable to choose the optimal element type and local mesh density.